<p>^^And for no. 2, think about it.
You have one plane, so no weird circles tilted by weird angles in midair or anything.</p>
<p>You have a specified center. You have a specified perimeter, and that means a specified radius. A circle in space is distinguishable from all the others by its center and radius. No two (different) circles can have the same center and radius in one plane.</p>
<p>Now of course if it was in a three-dimensional space, you could rotate that same circle on an axis and stuff, but that’s a bit beyond this problem…:)</p>
<ol>
<li>Because traffic was [unusually heavy], Jim arrived ten minutes late [for] his job interview even though he had [ran desperately] all the way [from] the bus stop.</li>
</ol>
<p>I put no error. The answer is [ran desperately]. I am assuming it should be even though he had RUN desperately. They both sound fine to me however. had ran…had run…jim had ran…jim had run. ???</p>
<hr>
<ol>
<li>At a time [when] interest in twentieth-century classical music [seems] on the verge [to disappear], the avant-garde compositions of the 1960s and 1970s [manage] to retain their popularity.</li>
</ol>
<p>I got this one right because the answer just pops out (to disappear) however the sentence still seems very awkward to me. With the correction, it would read…</p>
<p>At a time when interest in twentieth-century classical music seems on the verge of disappearing, the avant-garde compositions of the 1960s and 1970s manage to retain their popularity.</p>
<p>Cutting out the nonsense…</p>
<p>At a time when interest seems on the verge of disappearing, the compositions manage to retain their popularity.</p>
<p>Shouldn’t it be MANAGED? I guess not because of “seems” but this whole thing just sounds weird to me (maybe because of “at a time”).</p>
<p>For the cube problem, why isn’t the answer 90 degrees? Because AC is a diagonal of the square base, it bisects the right angles at A and C. The base angles are each 45 degrees, making AGC a right angle.</p>
<p>On number 4 how did you know the point was (-4,3)? I understand the perpendicular line and negative reciprocal slope but how did you get the 3? By using the origin again and solving for x with delta y over delta x? I think I may be missing something…</p>
<p>Plug in -4 in the x-coordinate in the original equation: x^2+y^2= 25
16+y^2=25
y^2=9
Y=3, -3
But since the point is above the x axis, the y coordinate must be 3.</p>